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Let b, c be positive integers, x 1 , x 2 be indeterminates over Z and x m , m ∈ Z be rational functions defined by x m−1 x m+1 = x b m +1 if m is odd and x m−1 x m+1 = x c m +1 if m is even. In this short note, we prove that for any m, k ∈ Z, x k can be expressed as a substraction-free Laurent polynomial in Z[x ±1 m , x ±1 m+1 ]. This proves(More)
One of the key challenges in current research into electromagnetic cloaking is to achieve invisibility at optical frequencies and over an extended bandwidth. There has been significant progress towards this using the idea of cloaking by sweeping under the carpet of Li and Pendry. Here, we show that we can harness surface plasmon polaritons at a metal(More)
We study cluster algebras associated to a quiver equipped with a group of admissible automorphisms. This enables us to realize cluster algebras of non simply laced types as quotients of cluster algebras of simply laced types. We then generalize well known results on cluster algebras as denominators theorems and, under some conditions, the linear(More)
Progress in Computational Fluid Dynamics (CFD) methods holds potential for the advancement of wind energy resource assessment in complex urban terrain by modeling wind circulation around urban obstacles. The geometry in urban areas is significantly more complex than for open rural spaces and has a critical influence on wind flow at the micro-meteorological(More)
The polyene antibiotic "Amphotericin B" can interact with sterols, cholesterol or ergosterol in aqueous and hydroalcoholic media and a correlative striking spectral change appears between 300 and 420 nm in the CD and absorption spectra. Using these spectroscopic methods we have determined that the influence of temperature between 4 and 80 degrees C is very(More)
We propose a numerical and an experimental study of an invisibility carpet for linear water waves. In the first part, we introduce the concept of an invisibility carpet in the case of linear water waves and apply this concept for a bounded problem: a wavetank. In the second part, we study a simpler case where we attempt to render invisible a vertical(More)
This paper extends the proposal of Li and Pendry [Phys. Rev. Lett. 101, 203901-4 (2008)] to invisibility carpets for infinite conducting planes and cylinders (or rigid planes and cylinders in the context of acoustic waves propagating in a compressible fluid). Carpets under consideration here do not touch the ground: they levitate in mid-air (or float in(More)
We extend the design of radially symmetric three-dimensional invisibility cloaks through transformation optics to cloaks with a surface of revolution. We derive the expression of the transformation matrix and show that one of its eigenvalues vanishes on the inner boundary of the cloaks, while the other two remain strictly positive and bounded. The validity(More)
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